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General Relativity and Quantum Cosmology

Title:
Celestial Ephemerides in an Expanding Universe

Abstract: Post-Newtonian theory was instrumental in conducting the critical
experimental tests of general relativity and in building the astronomical
ephemerides of celestial bodies in the solar system with an unparalleled
precision. The cornerstone of the theory is the postulate that the solar system
is gravitationally isolated from the rest of the universe and the background
spacetime is asymptotically flat. The present article extends this theoretical
concept and formulates the principles of celestial dynamics of particles and
light moving in gravitational field of a localized astronomical system embedded
to the expanding Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. We
formulate the precise mathematical concept of the Newtonian limit of Einstein's
field equations in the conformally-flat FLRW spacetime and analyze the geodesic
motion of massive particles and light in this limit. We prove that by doing
conformal spacetime transformations, one can reduce the equations of motion of
particles and light to the classical form of the Newtonian theory. However, the
time arguments in the equations of motion of particles and light differ from
each other in terms being proportional to the Hubble constant, H. This leads to
the important conclusion that the equations of light propagation used currently
by Space Navigation Centers for fitting range and Doppler-tracking observations
of celestial bodies are missing some terms of the cosmological origin that are
proportional to the Hubble constant, H. We also prove that the Hubble expansion
does not affect the atomic time scale used in creation of astronomical
ephemerides. We derive the cosmological correction to the light travel time
equation and argue that their measurement opens an exciting opportunity to
determine the local value of the Hubble constant, H, in the solar system
independently of cosmological observations.